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The geometric measure theoretical characterization of viscosity solutions to parabolic Monge-Ampère type equation. (English) Zbl 0811.35053
The authors develop a measure theoretic notion of weak solution for parabolic Monge-Ampère equations of the form \((*)\) \(-u_ t \text{det} D^ 2_ xu = f(x,t)\) which is completely analogous to that of Aleksandrov for elliptic Monge-Ampère equations. They also show that a continuous weak solution is a viscosity solution (and vice versa) if \(f\) is positive and continuous, and prove an existence and uniqueness result for the first initial-boundary value problem for \((*)\).
Reviewer: J.Urbas (Canberra)

35K55 Nonlinear parabolic equations
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games